Acceleration
Mechanics & Properties of Matter 2:
Acceleration
AIM
This unit defines acceleration and describes methods of measuring it. Graphical methods of
representing acceleration are considered.
OBJECTIVES
On completing this unit you should be able to:
• describe the principles of a method for measuring acceleration.
• state that acceleration is the change in velocity per unit time.
• sketch an acceleration-time graph using information obtained from a velocity-time
graph.
• use the terms ‘constant velocity’ and ‘constant acceleration’ to describe motion
represented in graphical or tabular form.
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Mechanics and Properties of Matter
Acceleration
Acceleration
Acceleration is defined as the change in velocity per unit time.
The unit is metre per second squared, ms-2.
a =
where
v - u
t
v = final velocity
u = initial velocity
t = time taken
Measuring acceleration
Acceleration is measured by determining the initial velocity, final velocity and time taken. A
double mask which interrupts a light gate can provide the data to a microcomputer and give a
direct reading of acceleration.
Acceleration-time and velocity-time graphs
Constant velocity
Constant positive acceleration
(velocity increasing)
v / ms -1
v / ms -1
t/s
Constant deceleration
Constant negative acceleration
(velocity decreasing)
v / ms -1
t/s
a / ms -2
a / ms -2
a / ms -2
t/s
a=0
t/s
t/s
t/s
acceleration is positive
acceleration is negative
Constant velocity and constant acceleration
The velocity time graph below illustrates these terms.
OA
v / m s -1
A
AB
B
BC
O
Strathaven Academy
C
t / s
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is constant acceleration,
the acceleration is positive.
is constant velocity,
the acceleration is zero.
is constant deceleration,
the acceleration is
negative.
Mechanics and Properties of Matter
Acceleration
ACTIVITY 1
Title: Acceleration
Aim: To calculate the acceleration of a trolley moving down a slope.
Apparatus: 2 light gates, 1 trolley, 1 slope, 3 stopcocks, 2 power supplies.
P o w e r s u p p ly
C ard
L ig h t g a t e
T im e r
( t2 )
T im e r
( t1 )
T im e r
( t3 )
Instructions
• Set up the apparatus as shown.
• Release the trolley from the top of the slope.
• When clock 1 starts, start clock 3 manually.
• When clock 2 starts, stop clock 3 manually.
• Repeat 5 times, ensuring the trolley takes the same path each time.
• Measure the length of the card.
• For each run calculate the acceleration.
• Find the mean acceleration and estimate the random uncertainty.
• Present your results in table form.
• Suggest how the experiment could be improved.
Run
t1
(s)
u
(ms-1)
t2
(s)
v
(ms-1)
t3
(s)
a
(ms-2)
Mean a
(ms-2)
1
2
3
4
5
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Mechanics and Properties of Matter
Acceleration
ACTIVITY 2A
Title: Acceleration
Aim: To measure the acceleration of a trolley moving down a slope using a computer.
Apparatus: 1 slope, 1 trolley and double mask, 1 light gate, computer and interface, (QED)
Apparatus: 1 power supply.
P o w er
C ard
s u p p ly
L ig h t
gate
In terface
C o m p u ter
Instructions
• Set up the apparatus as shown in the diagram.
• After selecting the acceleration program, allow the trolley to run down the track.
• Note the value of the acceleration.
• Repeat 5 times. Calculate the mean acceleration and random uncertainty.
• Explain, in detail, how the mask arrangement allows the computation of the
acceleration.
ACTIVITY 2B
Title: Acceleration
(Outcome 3)
Apparatus: as in Activity 2A
Instructions
•
For 5 different angles of slope find the corresponding acceleration.
• Using an appropriate format to find the relationship between the angle of slope and
the acceleration.
ACTIVITY 3
Title: Acceleration
Aim: To measure the acceleration due to gravity.
Apparatus: 1 light gate, 1 power supply, 1 metal mask, 1 computer and interface.
M e t a l p la t e
L ig h t g a t e
P o w e r s u p p ly
In terface
C o m p u ter
Instructions
• Set up the apparatus as shown in the diagram.
• Using the acceleration program, drop the mask, so it cuts the light beam.
• Repeat 5 times. Calculate the mean value of the acceleration and the random
uncertainty.
• Suggest any improvements to the experiment
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Mechanics and Properties of Matter
Acceleration
Speed
1.
The world downhill speed skiing trial takes place at Les Arc every year. Describe a
method that could be used to find the average speed of the skier over the 1km run.
Your description should include:
a) any apparatus required
b) details of what measurements need to be taken
c) an explanation of how you would use the measurements to carry out the
calculations.
2.
An athlete ran a 1500 metres race in 3 minutes 40 seconds. Find his average speed for
the race.
3.
How far away is the sun if it takes light 8 minutes to reach Earth?
(Speed of light = 3 × 108 ms-1).
4.
Concorde travels at an average speed of Mach 1.3 between London and New York.
Calculate the time for the journey to the nearest minute. The distance between
London and New York is 4800 km.
(Mach 1 is the speed of sound. Take the speed of sound to be 340 ms-1).
5.
The speed - time graph below represents a girl running for a bus. She starts from a
standstill at O and
jumps on the bus at Q.
v/ms-1
t/s
R
v
15
( m s -1 )
10
5
P
Q
O
2
Find:
a)
b)
c)
d)
e)
8
18
t (s )
the steady speed at which she runs
the distance she runs
the increase in the speed of the bus while the girl is on it
how far the bus travels during QR
how far this girl travels during OR.
6.
A ground-to-air guided missile accelerates from rest at 150 ms-2 for 5 seconds. What
speed does it reach?
7.
An Aston Martin accelerated from rest at 6 ms-2. How long does it take to reach a
speed of 30 ms-1?
8.
If a family car applies its brakes when travelling at its top speed of 68 ms-1, and
decelerates at 17 ms-2, how long does it take to reduce its speed by 34 ms-1?
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Mechanics and Properties of Matter
Acceleration
Acceleration
9.
An armour-piercing shell, travelling at 2000 ms-1, buries itself in the concrete wall of a
bunker. If it decelerates at 20000 ms-2, what time does it take to come to rest after
striking the wall?
10.
A skateboard running from rest down a concrete path of uniform slope reaches a speed
of 8 ms-1 in 4 s.
What is the acceleration of the skateboard?
How long after it started would the skateboard take to reach a speed of 12 ms-1?
11.
In the Tour de France a cyclist is travelling at 20 ms-1. When he reaches a downhill
stretch his speed increases to 40 ms-1. It takes 4 s for him to reach this point on the hill.
What is the acceleration of the cyclist on the hill?
Assuming he maintains this acceleration, how fast will he be travelling after a further
2 s?
How long would it take the cyclist to reach a speed of 55 ms-1?
12.
Use the information given below to calculate the acceleration of the trolley.
C lo c k
1
C lo c k
3
C lo c k
2
L ig h t g a t e s
Length of card = 5 cm
Time on clock 1 = 0.10 s (time taken for card to interrupt top light gate)
Time on clock 2 = 0.05 s (time taken for card to interrupt bottom light gate)
Time on clock 3 = 2.50 s (time taken for trolley to travel between light gates)
13.
A pupil uses light gates and a suitably interfaced computer to measure the acceleration
of a trolley as it moves down an inclined plane.
The following results were obtained:
acceleration (ms-2)
5.16, 5.24, 5.21, 5.19, 5.20, 5.20, 5.17, 5.19.
Calculate the mean valve of the acceleration and the corresponding random
uncertainty.
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Mechanics and Properties of Matter
Acceleration
Graphs
27.
The graph below shows how the acceleration of an object varies with time.
The object started from rest.
a / ms-2
4
2
0
10
5
t/s
Draw a velocity time graph for the first 10 s of the motion.
28.
The velocity time graph
for an object is shown below.
v / ms-1
Velocity
t/s
10
(m s -1)
5
0
2
3
10
4
3
Draw the corresponding acceleration-time graph.
(Put numerical values on time axis).
29.
The graph shows the velocity of a ball which is dropped and bounces from a floor.
A downwards direction is taken as being positive.
B
v / ms-1
t/s
+
E
0
D
-
C
a) During section OB of the graph
i) in which direction is the ball travelling?
ii) what can you say about the speed of the ball?
b) During section CD of the graph
i) in which direction is the ball travelling?
ii) what can you say about the speed of the ball?
c) During section DE of the graph
i) in which direction is the ball travelling?
ii) what can you say about the speed of the ball?
d) What happened to the ball at point B on the graph?
e) What happened to the ball at point C on the graph?
f) What happened to the ball at point D on the graph?
g) How does the speed of the ball immediately after rebound compare with the speed
immediately before?
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Mechanics and Properties of Matter
Acceleration
30.
Which velocity-time graph below represents the motion of a ball which is thrown
vertically upwards and returns to the thrower 3 seconds later?
31.
A ball is dropped from a height and bounces up and down on a horizontal surface.
Assuming that there is no loss of kinetic energy at each bounce, select the
velocity-time graph which represents the motion of the ball from the moment it is
released.
v / ms-1
v / ms-1
v / ms-1
t/s
A
v / ms-1
t/s
C
v / ms-1
0
D
32.
t/s
B
t/s
E
t/s
A ball is dropped from rest and bounces several times, losing some kinetic energy at
each bounce. Selected the correct velocity - time graph for this motion.
v / ms-1
v / ms-1
v / ms-1
t/s
t/s
A
t/s
B
v / ms-1
C
v / ms-1
t/s
t/s
E
D
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Mechanics and Properties of Matter